Call for Papers: Special Issue on Neural Networks Depicted in ODEs with Applications

Abstract

With the exponential growth in data availability and the advancements in computing power, the importance of neural networks lies in its ability to process large-scale data, enable automation tasks, support decision-making, etc. The transformative power of neural networks has the potential to reshape industries, improve lives, and contribute to the advancement of society as a whole. Neural networks depicted in ordinary differential equations (ODEs) ingeniously integrate neural networks and differential equations, two prominent modeling approaches widely applied in various fields such as chemistry, physics, engineering, and economics. Serving as equations that describe the relationship between a class of functions and their derivatives, ODEs possess rich mathematical analysis methods and are thus integral tools in classical mathematical theory. Neural networks depicted in ODEs leverage the differential equation description of physical processes, combining it with the potent fitting capabilities of neural networks. In contrast to traditional neural networks that overlook physical information and rely solely on numerous neurons for fitting, neural networks depicted in ODEs can achieve more accurate estimates with fewer neurons, while maintaining robustness, generalization, and interpretability in the learned systems. To fulfill the powerful potential of robots, plenty of algorithms based on neural networks depicted in ODEs are researched to simulate human-like learning processes, realize decision-making tasks, and address the issues of uncertain models and control strategies. Robots have great application value in the fields of artificial intelligence, information technology, and intelligent manufacturing due to their efficient perception, decision-making, and execution capabilities.